The state of Louisiana has been using instant runoff voting for some
overseas absentee ballots for federal and state elections since at
least the early 1990s.

Instant runoff voting in Louisiana is born out of administrative
necessity. Louisiana uses the ‘Cajun’ primary system for state and
federal offices: all voters select from all potential candidates of all
parties in the October primary election. If a candidate earns a
majority of the total votes in that election, that candidate wins. If
not, a runoff is held between the top two candidates of any party in
November. Federal races are conducted the same way, but because of a
Supreme Court ruling that the state could not hold decisive elections
before election day in November, they are now held on a
November-December schedule.

Election administrators (called parish registrars in Louisiana) face a
daunting challenge: two elections in a month. They barely have time to
declare the winners of the October primary election for state offices
and determine what state races will go to a final runoff before they
must print the November ballots with the federal primary and the state
runoff. Overseas absentee voters often would not have time to get the
November ballot in time to mail it back.

Instant runoff voting solves the problem. State law permits parish
registrars to send special absentee ballots overseas that use
preferential voting. See Revised Statutes 18:1306(4) below. Overseas
voters get two ballots, a white primary ballot and a green general
ballot. The white primary ballot is a plurality election – vote for one
candidate. The green general ballot uses preferential voting: voters
rank the candidates, just in case their first choice candidate does not
survive to the runoff election.

Back in Louisiana, if any races go to a runoff election, the registrar
opens up the green envelope and checks if the absentee voters’
first-choice candidate made it to the runoff election. If so, the vote
of the absentee Louisianan counts for that candidate. If not, the
registrar looks to the second-choice candidates on the ballot (marked
with a ‘2’). The top-ranked candidate in the runoff election earns the
vote.

Read an excerpt from the Louisiana statute below:

The secretary of state shall prepare a special absentee ballot for
candidates and constitutional amendments to be voted on in general
elections, subject to approval as to content by the attorney general.
This special ballot shall only be for use by a qualified voter who is
either a member of the United States Service or who resides outside of
the United States. Such special ballot shall contain a list of the
titles of all offices being contested at the primary election and the
candidates qualifying for the primary election for each office, and
shall permit the elector to vote in the general election by indicating
his order of preference for each candidate for each office. On the
special ballot shall also be printed each constitutional amendment to
be voted on in the general election. To indicate his order of
preference for each candidate for each office to be voted on in the
election, the voter shall put the number one next to the name of the
candidate who is the voter's first choice, the number two for his
second choice and so forth so that, in consecutive numerical order, a
number indicating the voter's preference is written by the voter next
to each candidate's name on the ballot. A space shall be provided for
the voter to indicate his preference for or against each constitutional
amendment contained on the ballot. The voter shall not be required to
indicate his preference for more than one candidate on the ballot if
the voter so chooses. The secretary of state shall also prepare
instructions for use of the special ballot.